Linear algebra, vector rows/column's question

1. The problem statement, all variables and given/known data
This is more of a general question that doesn't require any math. (at least I don't think so)

2. Relevant equations
Requires knowledge of linear algebra.

3. The attempt at a solution
Well, right now i'm learning about vector spaces. But when I was learning about vector rows and vector column's, I had this question that my book didn't talk about. If the vector row's and vector column's are components of a vector, where do the numbers come from? And I know about how you represent a vector on a xy plan. But where do the numbers come from the vector it's self?

Staff: Mentor

I don't know what you mean by vector rows and vector columns. (Note: in English we usually form the plural by adding the letter s, not 's.)

Are you confusing these terms with row vectors and column vectors? A row vector is one whose components are written horizontally, like this: (1 2 5). A column vector is one whose components are written vertically.

A vector space is made up of vectors of some kind, an addition operation, and a multiplication operation. A vector space is described as being "over a field" of some kind, where the field could be the real numbers or the complex numbers, or some other field. The components of the vector come from the field that is associated with the vector space.

One vector space is R2, with the field being the real numbers. A couple of vectors in this vector space are (0 0) and (2 sqrt(3)). Every vector space has a zero vector.

Another vector space is C3 over the complex numbers. An example vector in this space is (2 + 3.7i, -1 -i, 7). I added commas to make it easier to tell one component from another here.

English is my first language, I live in Indiana. I just made a mistake. Just like with the order of row vectors. And never mind, I just asked someone that goes to Purdue, he said that it was the length of the components of that vector measured in like x and y and z. So the numbers just represent the magnitude of the vector?